Rational Approximation Models of Fractional Butterworth Analog Filters

In recent years, fractional order based systems are playing a vital role in real time engineering problems. Rational approximation of 1.25, 1.5, 1.75 order Butterworth low pass and high pass filters proposed in this paper. The popular Matsuda and Oustaloup approximation methods are not give the better fitting with ideal one in specified frequency. Thus, a curve fitting (CF) approximation used to obtain the finite order transfer function without using Laplace operator <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$s^{m}$</tex>, where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$m$</tex> is the fractional order. Frequency response based CF method used to design fractional Butterworth filters and its efficacy compared with Matsuda based designs. The mean absolute error (MAE) and root mean square error (RMSE) values are tabulated to show the superiority of proposed CF approximation approach.